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This paper addresses adaptive channel estimation for time-varying mobile wireless channels with nonstationary statistics. We presents a reduced complexity adaptive channel estimator based on a set membership filtering approach known as the Optimal Bounding Ellipsoid (OBE) algorithm. To exploit time and frequency domain correlation properties of the channel in an efficient low-complexity way, we allow only a certain number of most significant channel impulse response taps to pass through time-domain adaptive filters while nulling the remaining taps. We obtain further complexity reduction by means of selective updating of the adaptive filters. Our proposed method overcomes the existing methodspsila drawbacks namely slow convergence, high sensitivity to channel statistics mismatch, and very high complexity. Comparisons with the existing methods (Robust MMSE estimator, adaptive NLMS and RLS estimators) corroborate advantages of our method in non-stationary time-varying wireless channels.